You might be surprised. The liquid-metal TaHfC pebble-bed reactor with a water-based exhaust of 5.4 km/s has a bare-bones TWR of 260:1, including the weight of the reactor, the turbopump, the nozzle, and the gimbal system, at a 12 kN vacuum thrust rating. Of course, that's without safety margins or shielding. But it's not outside the realm of possibility.

Using liquid water makes it very thrusty.

Not really surprised due to its density but I'd like to see what that does to it's Isp. NERVA was around 900secs.

Exhaust velocity is, as I note above, 5.4 km/s. So that's around 550 seconds. Obviously you can do much better at equivalent temperatures with LH2, but at greatly reduced thrust.

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I'd also like to see what you're using for the Isp curve for a deeply pre cooled airbreathing hydrolox design.

I was looking at partial airbreathing: a turboramrocket rather than something as complex as SABRE. I can do SABRE, though. Note that I'm using net effective Isp, subtracting intake drag. Here's the specific impulse curve for the precooled hydrolox turboramrocket:

One issue with doing SABRE-SKYLON is that I'd have to add in lift drag, which is an entirely different beast.

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I'd be very surprised if any TaHfC design expected the pebbles to melt. Their purpose in the original designs were increase the surface area and ensure fission product containment.

The design noted above was liquid-metal-fission fuel, so the TaHfC encapsulation shell encases the fuel pellets, which melt as soon as operating temperature is reached, but are contained by the shell.

Yeah, sorry; I just ripped isps from the SSMEs, the Merlin D, and the Raptor (projected). Is there a better list?

Well I suppose people might be arguing for using the RD-180 instead of the Merlin 1D. However the trade is that the TWR of M1D is more than 2x better than that of RD-180. It would be reasonable to look at both, I think.

I mean, in theory I could just look at the potential energy of each propellant choice and operate from that, since what I'm really looking for is minimum fuel fraction.

NH3 is actually not that great. It disassociates readily, but since N2 is heavier than O2 and water already has a pretty solid disassociation fraction at these operating temperatures, there isn't much of an improvement. Ammonia is much, much less dense than water, too, so that's a big issue for SSTO designs.

By any chance, has anyone ever put together the hoped for vehicle and engine mass and performance figures for Venture Star compared to how various X-33 systems were headed before cancellation? I know engine weight was coming in high.

Let's see -- it was supposed to be a one thousand tonne GLOW with seven linear aerospike engines producing 13.4 MN of thrust. It was to be planned with thrust reserves of around 16% to allow for an engine out. Ariane 5's Vulcain hydrolox GG engine has a TWR of around 84:1, which is probably close to the maximum you can get with hydrolox. An aerospike will necessarily be heavier, though. If we give it a 5% mass penalty, which is generous, our TWR drops to 79.8:1; to get the required thrust we'd need 19.9 tonnes of engine.

By my table, minimum fuel fraction for hydrolox is 89%, so that's 890 tonnes of propellant. Claimed payload to LEO was 20.4 tonnes.

This means that to make it work, they'd have 69.7 tonnes of mass for the tanks, the airframe, the TPS, the wings, and the landing gear.

Might want to look over the ESA NTER work using an NTR with an inductive heater augmentation. Helium gas power cycle direct drives a turbine with rotor mounted magnets, creating what they call a turbo-inductor which skips power conversion steps and gets up to tungsten melting temps. Would this nominally be a supercharged cycle, or parallel mixed cycle concept? The kicker is this turbo-inductor is before the nozzle, so in theory that leaves room for something crazy like backending it with a VASIMR-esque accelerator/nozzle since you are near plasma conditions.

Wow, that's beautiful! Of course this is all closed-cycle; the "turbine" doesn't actually interact with an airstream at all. But a very very cool design nonetheless.

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As a filler, how do beamed propulsion (laser/microwave) LH2 SSTO stacks compare for fuel fractions? If the engine is effectively offboard, doesn't that put an limit bounds on the fuel fraction graph?

Beamed power has basically the same fuel fraction as an NTR. That's the nice thing about solving for fuel fraction; you can substitute in your vehicle's structural fraction and engines.

NH3 is actually not that great. It disassociates readily, but since N2 is heavier than O2 and water already has a pretty solid disassociation fraction at these operating temperatures, there isn't much of an improvement. Ammonia is much, much less dense than water, too, so that's a big issue for SSTO designs.

NH3 is actually not that great. It disassociates readily, but since N2 is heavier than O2 and water already has a pretty solid disassociation fraction at these operating temperatures, there isn't much of an improvement. Ammonia is much, much less dense than water, too, so that's a big issue for SSTO designs.

The density is 68% of that of water which is less but not to the extreme of LH2 which is 10x worse.

Oh, whoops. My mistake.

Wonder what the difference is, then. Ammonia has an isp about 13% higher than water at lower operating temperatures, but that gap would narrow at higher temperatures, where water disassociates more readily. Thrust is pretty poor, though.

1) water-hydrogen variable mixture ratio NTR. Liftoff with just water to get better T/W, and then gradually switching to pure hydrogen to get better isp later

2) hydrolox-chemical-NTR-serial-hybrid rocket. Use NTR as "preburners" for chemical;

First NTR warming up separately both hydrogen and oxygen into as high temperature as it can sustain, and then putting them up together in the final combustion chamber to ignite the chemical reaction which further increases the temperature and exhaust speed. And if pure hydrogen-NTR still allows better isp, then use this hybrid more only early in the flight where this might allow much better T/W than pure hydrogen-NTR.

1) water-hydrogen variable mixture ratio NTR. Liftoff with just water to get better T/W, and then gradually switching to pure hydrogen to get better isp later

2) hydrolox-chemical-NTR-serial-hybrid rocket. Use NTR as "preburners" for chemical;

First NTR warming up separately both hydrogen and oxygen into as high temperature as it can sustain, and then putting them up together in the final combustion chamber to ignite the chemical reaction which further increases the temperature and exhaust speed. And if pure hydrogen-NTR still allows better isp, then use this hybrid more only early in the flight where this might allow much better T/W than pure hydrogen-NTR.

Both good ideas to be sure.

To your first suggestion: Switching propellants is promising, but implementing it is challenging. Getting a deep-cryo liquid and a room temperature liquid to flow through the same piping and turbopump is virtually impossible. I suppose you could have a heat exchanger to warm the hydrogen to an appropriate temperature, but then the poor thrust of an LH2 NTR is even worse.

More likely would be a transmix of water and ammonia. Water is already often used as a carrier for ammonia; in fact, pure ammonia is referred to as "anhydrous ammonia". Using a blend of water and ammonia that changes mixture ratio during flight would be a great way to get high thrust off the pad and high(er) specific impulse for the terminal part of the burn.

To your second suggestion: something very similar to this has already been proposed; it's called LANTR, or LOX-Afterburning Nuclear Thermal Rocket. Basically, it's a normal liquid hydrogen NTR (although any reducing propellant would work), but the nozzle has injectors which allow LOX to be pumped into the hot exhaust stream after the nozzle throat. The LOX ignites with the nuclear-heated hydrogen, boosting thrust by a factor of about 3 but only cutting specific impulse by about half. If the LOX was "preburned" by vaporizing it in a less energetic external coolant loop, I bet the performance could be even higher...though then your pump system is dealing with Very Hot LOX, which is not a nice thing to deal with at all.

More likely would be a transmix of water and ammonia. Water is already often used as a carrier for ammonia; in fact, pure ammonia is referred to as "anhydrous ammonia". Using a blend of water and ammonia that changes mixture ratio during flight would be a great way to get high thrust off the pad and high(er) specific impulse for the terminal part of the burn.

To your second suggestion: something very similar to this has already been proposed; it's called LANTR, or LOX-Afterburning Nuclear Thermal Rocket. Basically, it's a normal liquid hydrogen NTR (although any reducing propellant would work), but the nozzle has injectors which allow LOX to be pumped into the hot exhaust stream after the nozzle throat. The LOX ignites with the nuclear-heated hydrogen, boosting thrust by a factor of about 3 but only cutting specific impulse by about half. If the LOX was "preburned" by vaporizing it in a less energetic external coolant loop, I bet the performance could be even higher...though then your pump system is dealing with Very Hot LOX, which is not a nice thing to deal with at all.

The water/ammonia system is a nice idea. There is this: http://www.astronautix.com/o/okb-670.html which gives isp 430 (sl) / 470 (vac?) for mixed alcohol/ammonia fuel. Since this is from ~1958 the reactor operating temperature is probably a lot lower than you are assuming for your PBR. Still, hydrolox isp from a propellant that's a lot easier to deal with than LH2. Oh, I just found a reference to this in Rockets and People that says the propellant is heated to 3000K.

For LANTR, why would you put a turbopump after the cooling loop? Ideally you pump LOX into the cooling circuit and it partially/completely vaporizes on the way to the nozzle injection ports.

Yeah, sorry; I just ripped isps from the SSMEs, the Merlin D, and the Raptor (projected). Is there a better list?

Well I suppose people might be arguing for using the RD-180 instead of the Merlin 1D. However the trade is that the TWR of M1D is more than 2x better than that of RD-180. It would be reasonable to look at both, I think.

If you use the higher SL isp of the RD-180 along with the maximum theoretical vacuum specific impulse of kerolox (353 seconds), pure-rocket fuel fraction drops to 93.7%. That's without factoring in any increase in gravity drag from the slightly lower fuel consumption.

But you're right, the TWR is less than half (78.44 to the Merlin 1D's uprated 183). So based solely on dry mass considerations, the Merlin 1D still wins (5.53% of GLOW for payload, structure, and margins vs. the RD-180's 4.64%).

More likely would be a transmix of water and ammonia. Water is already often used as a carrier for ammonia; in fact, pure ammonia is referred to as "anhydrous ammonia". Using a blend of water and ammonia that changes mixture ratio during flight would be a great way to get high thrust off the pad and high(er) specific impulse for the terminal part of the burn.

The water/ammonia system is a nice idea. There is this: http://www.astronautix.com/o/okb-670.html which gives isp 430 (sl) / 470 (vac?) for mixed alcohol/ammonia fuel. Since this is from ~1958 the reactor operating temperature is probably a lot lower than you are assuming for your PBR. Still, hydrolox isp from a propellant that's a lot easier to deal with than LH2. Oh, I just found a reference to this in Rockets and People that says the propellant is heated to 3000K.

At lower temperatures, with less disassociation, ammonia beats water by 13%; at liquid-uranium pebble-bed reactor temperatures, I'm guessing the isp would go up by about 10%. The idea mixture ratio would have to be determined analytically, but if I model it as a gradual ramp-up from SL water ISP to vacuum ammonia ISP, (running pure ammonia through at around 50% of GLOW), then fuel fraction drops from 83.1% to 80.1%, which is helpful.

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For LANTR, why would you put a turbopump after the cooling loop? Ideally you pump LOX into the cooling circuit and it partially/completely vaporizes on the way to the nozzle injection ports.

Ah, yes, good point. Not sure what I was thinking there. Though you're still dealing with hot LOX in the nozzle injection ports.